# Is the moon's Hill Sphere the same as its Roche Radius?

• naranekkosh
In summary, the moon has a Roche limit, which is the distance at which an orbiting body will be pulled to the larger body. There are many variables that affect the limit of any particular orbiting body, including relative density and tensile strength. This will help: http://www.answers.com/topic/roche-limit

#### naranekkosh

does the moon hav it sown roghe radius? where objects need to be at a certain distance so that the gravity of the moon doesn't pull that object towards the moon? like an artificial communications satellite when we eventually colonize the moon...what is the distance a satellite needs to be to avoid being pulled in. does it matter on that size/mass of the artifical satellite?

naranekkosh said:
does the moon hav it sown roghe radius? where objects need to be at a certain distance so that the gravity of the moon doesn't pull that object towards the moon? like an artificial communications satellite when we eventually colonize the moon...what is the distance a satellite needs to be to avoid being pulled in. does it matter on that size/mass of the artifical satellite?
The Roche radius is not a fixed barrier below which an orbiting body is pulled to the larger body. It is the critical distance closer than which an orbiting body will be tidally disrupted and torn apart by the larger body. There are many variables that affect the limit of any particular orbiting body, including relative density and tensile strength. This will help:

Perhaps you should look instead at the Hill Sphere, the approximate distance from the moon at which a satellite could have a stable orbit. It's somewhat related to the Roche lobe, so maybe that's what you were thinking of. Anyway, it would be given by:

$$r=r_m(\frac{M_m}{3(M_m+M_e)})^{1/3}$$

This gives a distance of 15% the distance between the Earth and the moon (~60,000 km). There would be other corrections due to the sun's gravity, however, and I won't try to approximate those.

Oh, and for any reasonably-sized satellite, this wouldn't depend on the properties of the satellite.

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SpaceTiger said:
Perhaps you should look instead at the Hill Sphere, the approximate distance from the moon at which a satellite could have a stable orbit. It's somewhat related to the Roche lobe, so maybe that's what you were thinking of. Anyway, it would be given by:

$$r=r_m(\frac{M_m}{3(M_m+M_e)})^{1/3}$$

This gives a distance of 15% the distance between the Earth and the moon (~60,000 km). There would be other corrections due to the sun's gravity, however, and I won't try to approximate those.

Oh, and for any reasonably-sized satellite, this wouldn't depend on the properties of the satellite.
Thanks for infro - I had never heard of "Hill Sphere" before, but knew about Roche limit. I believe R.L. sets a limit on when the Earth got it's moon as reversing time and making reasonable assumptions about tidal dissipation, torques, land /water geometry, etc. one can calculate how long ago the moon would have been at the Roche limit. Days would have been much shorter then and tides much larger.
I think the Earth is older, so we definitely got it later, not at same time as Earth was forming. I also think I have read that the tides would have been more than 100 feet of tide in open ocean. -Do you know anything about this? With two large tides coming every day (of much less than 24 hours) it seems very reasonable that life in the water would be the obvious choice, but I don't know much about how this "short days/ large tides" period relates to the origin of life.

Also there may be another limit of interest. Like Roche limit, its value would depend upon the particular body orbiting. Thus I will assume a "dumb bell" of two equal masses separated by a semis-rigid rod of 100 feet (or meters, if you like). Rod is "semi-rigid" so when it flexes, it dissipates energy. In the moon's gravity gradient the dumb bell can have the rod axis pointing at the center of the moon, provided it is orbit about the moon and not too far from moon. (assume circular orbit)

My second question (and assumption) is about the maximum altitude of the dumb bell in which it is stably pointing at the moon. (good for communication antennas relaying msg between settlements in different locations) Is it the same as the Hill limit or smaller? (Lets neglect the Earth.) Know any thing about this?

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## 1. What is the moon's Roche radius?

The moon's Roche radius is the distance from the center of the moon at which tidal forces from a larger body, such as the Earth, would overcome the gravitational pull of the moon and cause it to break apart.

## 2. How is the moon's Roche radius calculated?

The moon's Roche radius can be calculated using the formula R = 2.44 x (m/M)^(1/3) x r, where R is the Roche radius, m is the mass of the moon, M is the mass of the larger body, and r is the distance between the two bodies.

## 3. What factors affect the moon's Roche radius?

The moon's Roche radius is primarily affected by the mass of the moon and the larger body, as well as the distance between the two bodies. Other factors that can influence the Roche radius include the density and composition of the two bodies.

## 4. Can the moon's Roche radius change over time?

Yes, the moon's Roche radius can change over time due to factors such as changes in the moon's mass or the orbit of the larger body. It can also be affected by external forces, such as gravitational interactions with other celestial bodies.

## 5. How does the moon's Roche radius affect the formation of planetary rings?

The moon's Roche radius plays a significant role in the formation and structure of planetary rings. If a moon's Roche radius lies within the rings of a larger body, the tidal forces will cause the rings to spread out and eventually merge with the moon. If the Roche radius lies outside the rings, the rings will remain intact. This phenomenon can also create gaps and divisions within the rings.